I've just upgraded to the LTS and now I can't watch any videos on Your Tube via Flash in either Firefox or Chrome.

I had the issue with Chrome before I upgraded, but I could still see them in Firefox without an issue and I figured the upgrade would fix this.

I am getting the error message 'The Adobe Flash plug-in has crashed' and then underneath the viewing panel it says 'Upgrade to Flash Player 10 for improved playback performance. Upgrade Now or More Info.'

I have checked in the software centre and it is showing a green tick next to Adobe Flash plug-in for Mozilla.

I had some problems with Flash at first, and this solved them. Then I had some minor transitional issues after the fix, but some Firefox updates solved them and now it works perfectly (I use Ubuntu 10.10, however).

Its not clear if your running 32-bit or 64-bit. However i have the same problem that re-occurs everytime an update comes in that upgrades the flash-plugin package. For 64-bit initially check your /usr/lib/nspluginwrapper/i386/linux/npviewer setting is as in this post